The Prime Minister had come under pressure from unions, the Labour Party and the SNP to scrap the charge, as well as from a growing number of Conservative backbench MPs.
Downing Street said the Prime Minister has asked officials at the Home Office and the Department for Health and Social Care to remove health and care workers from the surcharge "as soon as possible".
Full details will be announced in the coming days, a Number 10 spokesman said.
Mr Johnson "has been thinking about this a great deal" and as a "personal beneficiary of carers from abroad" he understands the difficulties faced by our amazing NHS staff, the spokesman said.
"The purpose of the NHS surcharge is to benefit the NHS, help to care for the sick and save lives.
"NHS and care workers from abroad who are granted visas are doing this already by the fantastic contribution which they make."
The £400 surcharge remains in place for other categories of visa applicants and will increase to £624 in October, as planned.
The change will apply to all NHS workers, ranging from medical health staff to vital porters and cleaners.
It also includes independent health workers and social care workers.
Conservative MP and Public Administration and Constitutional Affairs Committee chairman William Wragg had called for an immediate change in policy, adding "now is the time for a generosity of spirit towards those who have done so much good".
At Prime Minister’s Questions on Wednesday, Mr Johnson was challenged by Labour leader Sir Keir Starmer, but defended the charge.
“I have been a personal beneficiary of carers who have come from abroad and frankly saved my life,” the Prime Minister said. “I know exactly the importance of what he asks.
“On the other hand, we must look at the realities. This is a great national service—it is a national institution—that needs funding, and those contributions help us to raise about £900 million.
“It is very difficult in the current circumstances to find alternative sources, so with great respect for the right honourable and learned gentleman’s point, I think it is the right way forward.”
It later emerged that the cost of waiving the surcharge for health and care workers was just £90 million per year.
The surcharge was also raised at PMQs by the SNP’s Westminster leader Ian Blackford, who said the Prime Minister should be “embarrassed that this is how his Government choose to treat NHS and care workers”.
Responding to the u-turn, Mr Starmer said: "This is a victory for common decency and the right thing to do. We cannot clap our carers one day and then charge them to use our NHS the next." Mr Blackford said the surcharge should be scrapped altogether.
British Medical Association council chairman Dr Chaand Nagpaul said: "It's absolutely crucial, that we recognise and value healthcare workers from overseas, who as this pandemic has clearly highlighted, provide an invaluable service protecting and looking after the health of our nation.
"The scrapping of the surcharge must come into effect immediately to show our gratitude for the effort and dedication our overseas workers give to the NHS and to their patients."
The Royal College of Nursing's Dame Donna Kinnair said: "Scrapping the unfair Immigration Health Surcharge is something our members have been demanding for two years.
"I welcome the news on their behalf, but it is a shame it took this pandemic for the Government to see sense."
Unison general secretary Dave Prentis said: "This is long overdue. The pandemic has shown the enormous contribution of overseas workers to our health and care system."
The U-turn came hours after Downing St insisted the PM was standing by the surcharge.
It also came a day after another U-turn when the Government extended a scheme offering indefinite leave to remain to the families of all NHS staff who die as a result of contracting coronavirus.
Care workers, cleaners and porters had originally been left out of the scheme, which only applied to certain occupations including nurses, biochemists and radiographers.
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